Members of the public reported seeing a boy who was "small in build and alone" in West Pilton Gardens, Edinburgh, at around 8.30am yesterday morning.
The timing of the sighting has been confirmed by CCTV but it cannot confirm the identity of the child, Police Scotland said.
Mikaeel disappeared from his home in the Scottish capital after being put to bed on Wednesday night.
Hundreds of people have joined in the search for the missing youngster as police said they are becoming increasingly concerned.
Officers are now asking for the public's help in light of the possible sighting.
Police want anyone else who saw the child to get in touch urgently as they work to confirm whether it was Mikaeel or another youngster.
They said the small boy matched the description of Mikaeel, although the child was also wearing a cap or hat.
Superintendent Liz McAinsh said: "Since Mikaeel was reported missing, we have been contacted by a number of people with information which we have been working to assess and respond to.
"Members of the public have come forward to report seeing a boy walking in the vicinity of West Pilton Gardens at 8.30am yesterday.
"The witnesses were in a vehicle driving down West Pilton Gardens at the time they saw the boy.
"They described seeing a small boy on the right-hand side pavement running towards the junction with West Pilton Park.
"They noticed him because he was small in build and alone at the time. They said he matched the description given of Mikaeel, although they also reported the child they saw was wearing a cap or hat."
She added: "We would ask that anyone who also saw this child contact us as a matter of urgency. We need to confirm if this was Mikaeel or if it was another child. If it is your child who was out at this time and in this location, we want to hear from you so we can eliminate this line of inquiry as swiftly as possible."
Anyone with information relating to this sighting is being asked to contact the dedicated telephone number 0300 200 0200.
Hundreds of people have turned out in unprecendent push to find the missing three-year-old.
People have gathered at the West Pilton Neighbourhood Community Centre in Edinburgh as the search for the youngster continues.
Mikaeel disappeared from his home after being put to bed on Wednesday night and hasn't been seen since.
Douglas Nairn, 60, who has come to the community centre to help search, said: "It's a three-year-old boy. There's a possibility that he doesn't know where he is or what's happening to him. I will stay out as long as it takes."
Leone Bissette, 34, who has come down to the centre with her 11-month-old daughter Katie, said: "We came just to see what we could do.
"If it was me I would hope people would want to help.
"We just want to be any help that we can. We are just trying to give as much time as we can."
Kenny Turner, 55, from Granton, said: "I feel for the family. When you've got kids and grandkids of your own you know what they are going through. I hope he is found and he is safe and well."
Nicola Hunter, 31, from Muirhouse has two sons, aged 11 and five. She said: "I am a mum and I just want to try and help. It's every mum's worst nightmare. It's just too close to home, to think that he was out there last night."
Kimberly MacFadyen, 34, from Davidson's Mains, has a five-year-old boy. "I would be absolutely devastated if it was my wee boy and I would want every person in Edinburgh to stop what they were doing and come to look for him," she said. "Everyone is pulling together it seems. Everyone is talking about it at school and about what they are trying to do."
Members of the local community who want to help with the search today are asked to go to the premises at North Neighbourhood Centre at West Pilton Gardens at 10am dressed in warm clothes and sturdy footwear.
Mikaeel Kular was reported yesterday.
A major ground, air and sea search has so far failed to find any sign of him.
Police Scotland superintendent Liz McAinsh said: "We are obviously deeply concerned that we have had no sightings of Mikaeel. All lines of inquiry in the investigation remain open, we are pursuing many lines of inquiry.
"I would ask anyone who has got any information to get in touch with us.
"We still have no evidence of any criminality at this point."
Family members were joined by neighbours and emergency services as they searched through the night for him as temperatures plunged to just above freezing.
The boy's mother has been named locally as Rosdeep Kular, 33.
Ms McAinsh said: "Mikaeel's mother is getting a lot of support from both the police, her family and her friends but clearly she is very distraught, she just wants her little boy back home with his brothers and sisters. We are very concerned for her. We just want to be able to give her some news or let her know he is safe and well."
She said that officers have spoken to Mikaeel's father and that all of the boy's family have been very helpful to the police.
She added: "No-one is detained, no-one is a suspect, we have no evidence of any criminality."
Asked whether she thinks the child will be found alive and well she said: "I remain optimistic but as time passes we become deeply concerned. I would stress that this is still a missing person inquiry and we are treating it as such. We have no evidence of criminality although all lines of inquiry are being progressed but of course we remain concerned, we just want to find Mikaeel safe and well and that's why we're urging members of the public to assist us."
Ms McAinsh urged people to remain vigilant and to search any areas they may have searched yesterday
She said: "Check your local premises, check your gardens, check your shed, check your car, check anywhere where a wee three-year-old boy who may have been out and about would find some shelter."
Hundreds of officers are involved in the search and specialist search teams, mounted officers, dogs, other emergency services and local organisations will also be involved in the investigation today.
Ms McAinsh said more than 150 calls had been made to the helpline which has been set up but there have been no confirmed sightings yet.
CCTV from the scene has been examined but has turned up "nothing significant" so far, she said.
She said she was not aware of any tension in the family that would have caused Mikaeel to run away.
She added: "We have spoken to his father. All of his family have been very, very helpful to the police. They continue to help us with our inquiries and obviously we are keen to get as much information as we can from them as we just never know who might hold that vital bit of information that will help us find him."
Mikaeel's mother put him to bed at around 9pm on Wednesday only to find his room empty when she checked at about 7.15am yesterday.
The little boy, who has two sisters and two brothers, usually sleeps in the same room as his twin sister but was alone on Wednesday night.
His jacket and shoes were missing and police are looking into whether he might have left of his own accord.
Ms McAinsh said police have spoken to all close members of the boy's family who are assisting police.
Mikaeel is slim, 3ft, of Asian appearance and possibly wearing a thigh-length beige hooded coat.
He may also be wearing black gloves with multi-coloured fingers, dark navy blue jogging bottoms, a grey pyjama top with an embroidered turquoise dinosaur on the chest and brown Clarks shoes.
He has a faded scar on the bridge of his nose and a sore on the left hand side of his mouth.
Police last night issued a new photograph of the missing boy, showing him in the beige jacket he was believed to be wearing when he disappeared.
Yesterday police detained a man in the city's Waterfront Gait but said it was unconnected with the boy's disappearance.
Police have activated the Child Rescue Alert system, which is usually reserved for abduction and kidnap cases and supported by all police forces across the UK.
A special telephone number has been set up for anyone who has seen the child or has information about his whereabouts. Calls to the 0300 200 0200 number will be answered by dedicated members of staff.
The temperature in Edinburgh dropped to a low of 2.7C overnight.
Large sections of Ferry Gait Crescent remain cordoned off and police officers are stationed outside several of the modern blocks of flats, including the one containing the family's home.
The windows of the flat have been covered up to protect the family's privacy.
One neighbour Tracy Johnston, 45, said the community was in shock.
"It's pretty horrific. I've been up since the back of 6am and most of the lights have been on which is unusual.
"I don't think anyone slept very well last night. There are hundreds of people with kids here.
"I used to see the wee boy, he used to come up to the window with all the kids to get a biscuit."
l The national Child Rescue Alert can be reached on 0300 200 0200.
Here is a timeline of events surrounding the disappearance of missing three-year-old Mikaeel Kular.
Wednesday January 15
9pm: Mikaeel is last seen going to bed at his home address in Ferry Gait Crescent, Edinburgh.
Thursday January 16
4am: Temperatures drop to 2.3C (36F), according to Met Office figures.
7.15am: Mikaeel's mother discovers he is missing from his bed.
9am: Police Scotland reveal that they have launched a search for the boy. A large hunt is well under way in the Drylaw area and officers are assisted by a police helicopter.
10.20am: Police release an image of the missing boy, who is described as being of Asian appearance and possibly wearing a beige hooded jacket, blue jogging bottoms, brown shoes and nightwear.
10.55am: Police Scotland superintendent Liz McAinsh tells reporters there is no evidence to suggest criminality but officers are "keeping an open mind". It emerges that Mikaeel's jacket and shoes are not within his home. Police are looking into whether the boy may have left the home of his own volition. People in the local area are urged to look in their gardens, sheds and any areas where a three-year-old might go. The boy's mother is said to be distraught.
1.20pm: The detention of a man near Mikaeel's home is not connected with the police inquiry, officers say. A large media presence had gathered in the area around Waterfront Gait, where the man was detained.
2.30pm: Coastguard teams and lifeboats search the shoreline in the Cramond and Drylaw area. Neighbours and individuals have also been out searching throughout the day. In the House of Commons, Edinburgh MPs Mike Crockart and Mark Lazarowicz express their hopes Mikaeel would be safely returned to his family.
4pm: A dedicated telephone line is established as part of a Child Rescue Alert, supported by all police forces across the UK. The number is 0300 200 0200.
4.30pm: People are asked to urgently check all property including gardens, outbuildings, garages, sheds and vehicles for the youngster as darkness falls. Police issue an updated description of Mikaeel, adding that he has a faded scar on the bridge of his nose and a sore on the left hand side of his mouth.
5pm: A full-scale search involving the emergency services and worried neighbours continuing through the evening and into the night as concern grows for Mikaeel.
6.30pm: Gritters are seen out on the streets of Edinburgh, in preparation for a cold night ahead.
9pm: A new image of missing Mikaeel is released by Police Scotland. It shows him in the beige jacket he was believed to be wearing when he disappeared.
Friday January 17:
Overnight: Neighbours and the emergency services search through the night for the child but there is still no trace of him.
7am: Supt McAinsh say there has been a "fantastic" response from the public and urged anyone with information to contact them.
The search, using specialist officers, police dogs and horses and the air support unit, continues. Police are now said to be "deeply concerned" as they make a fresh appeal for help to find the three-year-old. It emerges that more than 150 calls have been made to the helpline but there have been no confirmed sightings.
10am: Hundreds of people gather at the North Neighbourhood Centre in West Pilton Gardens to help search for Mikaeel.
10.30am: Work is under way to publish a missing person appeal for Mikaeel on digital billboards across the UK. The adverts are expected to be shown in areas such as train stations and shopping centres.